〈a, b | aaa=1, babb=aba〉

Monoid presentation of length 10

Properties

Finite non-commutative monoid with 339 elements

Completion parameters

Reduction order: left-to-right b/a

Complete rewriting system

b⁷ ⇒ b
bab⁶ ⇒ ba
b⁶a ⇒ ab⁶
aba ⇒ bab²
ba²b⁶ ⇒ ba²
bab³a ⇒ (ab²)²
b⁵ab²a ⇒ ab³ab⁴
a³ ⇒ 1
a²b²a ⇒ (bab⁴)²
a²b⁴a ⇒ b³ab⁴ab⁵
a²b⁵a ⇒ b²a²b⁵
ab²a² ⇒ b⁵ab
ab³ab⁴a ⇒ b⁴ab
ab³ab⁵a ⇒ b⁴ab²ab⁴
ab⁴a² ⇒ b⁵a²b
ab(b⁴a)² ⇒ (b⁵a)²b
ba(b²a)² ⇒ ab(bab⁴)²
bab²ab⁴a ⇒ (ab⁴)³b
bab²ab⁵a ⇒ ab³a²b⁵
ba(b⁵a)² ⇒ a²b³ab²
b²a²b³a ⇒ a(b⁵a)²b
b³ab⁴ab⁵a ⇒ ab⁵a²b
b³ab⁵a² ⇒ ab⁴(ab⁵)²
(b⁴a)³ ⇒ ab(b²a)²b
a²b³a² ⇒ ba(b⁴ab)²
a²b(b²a)² ⇒ (b³ab)²bab⁴
a(b²ab²)²a ⇒ b²ab⁵a²b³
ab²ab⁴ab⁵a ⇒ (b²ab²)²ab⁵
ab²ab⁵a² ⇒ b²ab³(bab⁴)²
a(b⁴a)²b²a ⇒ (b²ab²)³

Idempotents

2 elements

1
b⁶

Right Cayley graph

Left Cayley graph

Others with same cardinality

4 unique, 5 total

Length:	Presentation:	Description:	Related:
10	〈a, b \| aaa=1, ababba=b〉	Finite non-commutative monoid with 339 elements	1 isomorphic
11	〈a, b \| aaa=1, abaabba=b〉	Finite non-commutative monoid with 339 elements
11	〈a, b \| aaa=1, abbab=baa〉	Finite non-commutative monoid with 339 elements
11	〈a, b \| aaa=1, baabb=aba〉	Finite non-commutative monoid with 339 elements

Other isomorphic instances

1 total

Length:	Presentation:
11	〈a, b \| aaa=1, aababb=ba〉

Other anti-isomorphic instances

1 total

Length:	Presentation:
11	〈a, b \| aaa=1, aabbab=ba〉